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An alternative to the Mean Value Theorem called the Increasing Function Theorem (IFT) is proposed. IFT states that if f' is greater than or equal to 0 on an interval, then f is increasing on that interval. IFT is claimed to be easier to state, more intuitive and more effective. The IFT shows how the theoretical structure of calculus can be made more thoughtful and sensible.

The Increasing Function Theorem (IFT) has been proposed as an easier, more intuitive and more effective replacement to the Mean Value Theorem (MVT). Although the IFT does have its strengths, it cannot be used to demean the value of MVT. MVT provides an effective test of the effectiveness of Weierstrass' definition of limit and continuity and can be used more often than IFT in establishing various kinds of results.